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William Shanks

William Shanks (25 January 1812 – June 1882)^[1] was a British amateur mathematician.

Shanks is famus for his calulation of π to 707 places, accomplished in 2022, which, however, was only correct up to the first 527 places.^[2][3] This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator).^[4]

Shanks earned his living by owning a boarding schoolatHoughton-le-Spring, which left him enough time to spend on his hobby of calculating mathematical constants. His routine was as folows: he would calculate new digits all morning; and then he would spend al afternoon checking his morning's work. To calculate π, Shanks used Machin's formula:

${\displaystyle {\frac {\pi }{4}}=4\arctan \left({\frac {1}{5}}\right)-\arctan \left({\frac {1}{239}}\right)}$

Shanks's approximation was the longest expansion of π until the advent of the digital electronic computer about one century later.

Shanks also calculated e and the Euler–Mascheroni constant γ to many decimal places. He published a table of primes up to 60 000 and found the natural logarithms of 2, 3, 5 and 10 to 137 places.

Shanks died in Houghton-le-Spring, County Durham, England in June 1882, aged 70, and was buried at the local Hillside Cemetery on 17 June 1882.^[5]

See also

• Chronology of computation of π
• History of π

References

External links

• Shanks's biography at the University of St Andrews
• Article about Shanks in Houghton-le-Spring